A lower bound of \(\widetilde{\operatorname{CV}}^O_{\mathrm {mod}}(L) - \widetilde{\operatorname{CV}}^O_{\mathrm {mod}}(K)\)  is developed in [1]} (see (REF ) below) where a simplifying assumption is made that
change-points do not occur at odd locations.
This additional assumption ensures that the first term in \(\operatorname{CV}_{(2)}(L)\)  is identical to \(\widetilde{\operatorname{CV}}^O_{\mathrm {mod}}(L)\)  as claimed by their second displayed formula on pg 433, where it is assumed that \(O_i\)  and \(E_i\)  have the same expectation.
As discussed at the beginning of the proof of Theorem 1 on pg. 8 in the supplemental material in [2]}, such an assumption may be justified when the noise variance is bounded away from zero and the signal magnitude is bounded; we however do not make these assumptions in our results in order to maintain greater fidelity to phenomena observed in finite sample settings.
